A direct memetic approach to the solution of multi-objective optimal control problems

Vasile, Massimiliano and Ricciardi, Lorenzo; (2017) A direct memetic approach to the solution of multi-objective optimal control problems. In: 2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016. Institute of Electrical and Electronics Engineers Inc., GRC. ISBN 9781509042401 (https://doi.org/10.1109/SSCI.2016.7850103)

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This paper proposes a memetic direct transcription algorithm to solve Multi-Objective Optimal Control Problems (MOOCP). The MOOCP is first transcribed into a Non-linear Programming Problem (NLP) with Direct Finite Elements in Time (DFET) and then solved with a particular formulation of the Multi Agent Collaborative Search (MACS) framework. Multi Agent Collaborative Search is a memetic algorithm in which a population of agents combines local search heuristics, exploring the neighbourhood of each agent, with social actions exchanging information among agents. A collection of all Pareto optimal solutions is maintained in an archive that evolves towards the Pareto set. In the approach proposed in this paper, individualistic actions run a local search, from random points within the neighbourhood of each agent, solving a normalised Pascoletti-Serafini scalarisation of the multi-objective NLP problem. Social actions, instead, solve a bi-level problem in which the lower level handles only the constraint equations while the upper level handles only the objective functions. The proposed approach is tested on the multi-objective extensions of two well-known optimal control problems: the Goddard Rocket problem, and the maximum energy orbit rise problem.